The noun steam refers to water in its gaseous form, but does it connote only the hot gas achieved (for example) from boiling, or does it equally connote the vapour that rises from an open body of cold water in colder temperatures?

Well, I call the vapour that rises from an open body of cold water mist, but some people do call it steam.
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Peter Shor Apr 10 '12 at 12:29

Am I the only one to be bothered by the use of connotation when (in my opinion) denotation or meaning appear more appropriate?
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Eugene SeidelApr 14 '12 at 8:37

You may be right. As far as I could tell, steam meant water in its gaseous form, but I've now learned a great deal more about its denotation than I ever could have imagined! But what I wanted to get at was what it means to people who use it (or hear it) -- its connotation.
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JAMApr 15 '12 at 15:29

5 Answers
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To answer your question, does the word steam equally connote the vapor that rises from an open body of cold water in colder temperatures: yes. Just Google "steam rising from a lake" and you will see all sorts of photos and videos and poetic descriptions about the vapor that appears over bodies of water in the morning. I don't know if the term is being used correctly (from a scientific standpoint), but people surely do use the word steam in the way that you describe.

It is actually much more common to speak of something "steaming" when it is emitting mist (droplets of liquid-phase water suspended in air) than when actual steam (involving gaseous-phase water) is being produced. Hardly anybody actually cares about the pedantic point involved.

Two definitions of steam, as given by the New Zealand Oxford Dictionary, are "a mist of liquid particles of water produced by the condensation of this gas [water vapour]" and "any similar vapour". When I went to school, our science teachers always stressed this as the correct definition of steam - the gaseous phase of water is called "water vapour", not "steam". Maybe times have changed, and definitions have loosened, but I've always been pedantic about only saying "steam" for the mist that you can actually see.

For example, when you boil water in a jug, you get visible clouds of steam; but between the top of the spout and the bottom of the steam clouds, there's a wee gap, where there is invisible water vapour.

I think your New Zealand science teachers were using a definition not endorsed by U.S. science teachers; we were taught that when water boiled, it turned into steam. Merriam-Webster has 2 a : the invisible vapor into which water is converted when heated to the boiling point b : the mist formed by the condensation on cooling of water vapor.
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Peter Shor Apr 10 '12 at 11:27

the vapor into which water is converted when heated, forming a white mist of minute water droplets in the air

the invisible gaseous form of water, formed by boiling, from which this vapor condenses

Steam is a technical term used to water vapor obtained when water boils. This is because there isn't any technical application of water vapor not obtained by boiling water; water vapor not obtained from boiling water is not useful for electricity production, or to power locomotives.

It depends on the context. You know there's a thing called dry steam.
In casual speech, steam refers to 'water vapour' (another flexible term), the hot liquid-gas phase, esp. a visible one.
Technically, steam may be understood mostly as water molecules above 100°C.
Evaporation takes place at all temperatures. Surface water from lakes rises into atmosphere all the time. However, we don't call that steam.